In a large saucepan, heat the olive oil over medium-high heat. Add the onion, carrot, and celery and cook, stirring frequently, until just tender, 5 to 7 minutes. Add the garlic and cook, stirring constantly, until fragrant, 30 seconds.
Add the diced tomatoes, broth, oregano, pepper, and basil, and bring to a boil.
Reduce the heat and let simmer for 10 minutes.
Add the salmon, rice, and broccoli; stir; Cook for 5 minutes.
To serve, ladle the soup into bowls and top each with 1 tablespoon Parmesan and chopped fresh basil.